Complex Systems

A New Game of Three-Dimensional Life Download PDF

Carter Bays
University of South Carolina, Columbia, SC 29208 USA


The three-dimensional cellular automaton known as Life was first reported in references [1] and [2]; at that time, two rules were described. These rules (also called "games of Life'') are known as Life 4555 and Life 5766, where the first two numbers give the "safe environment'' range (the number of live neighbor cells, represented as unit cubes, that must touch a currently live cell so that it will remain alive next generation) and the second two numbers specify the "fertility'' range (the number of live touching neighbors required to bring a currently dead cell to life next generation). It is possible to give a somewhat formal definition to rules that qualify as "games of Life''; this was done in [1] and the definition is repeated here.